Compositional Data in Biomedical Research

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Modern methods of compositional data analysis are not well known in biomedical research.
Moreover, there appear to be few mathematical and statistical researchers
working on compositional biomedical problems. Like the earth and environmental sciences,
biomedicine has many problems in which the relevant scienti c information is
encoded in the relative abundance of key species or categories. I introduce three problems
in cancer research in which analysis of compositions plays an important role. The
problems involve 1) the classi cation of serum proteomic pro les for early detection of
lung cancer, 2) inference of the relative amounts of di erent tissue types in a diagnostic
tumor biopsy, and 3) the subcellular localization of the BRCA1 protein, and it's
role in breast cancer patient prognosis. For each of these problems I outline a partial
solution. However, none of these problems is \solved". I attempt to identify areas in
which additional statistical development is needed with the hope of encouraging more
compositional data analysts to become involved in biomedical research
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